Plane Trigonometry, Mensuration, and Spherical Trigonometry

... plane and spherical ; and , in general , teaches to find , from three given parts of a triangle ( of which , however , in plane triangles , one at least must be a side ) , the three remaining parts . The application of Plane Trigo ...

... oblique cone which is made by a plane parallel to its base , is a circle having its centre in the axis of the cone . See the demonstration of Prop . 11 . PROP . 23 . In an oblique cone , if V A , V A ' are the slant sides in which the ...

... 10 , 4 , and 7 , and the perpen- dicular is let fall from the angle included ... PERIMETERS AND RECTIFICATION . AREAS OF SIMILAR FIGURES . BISECTORS OF THE ... Perimeters of Cor . 1. As squares of diagonals . Cor . 2. Regular polygons ...

... PS 90 ° - B PS 90 ° = - B β = BL = 90 ° + L — п SPP1 SP , P 180 ° - = --- L , B , = 180 ° — - ( 90 ° ) 90 ° ( λ — 11 — ↓ 1 ) so that , by the fundamental equations of Sph . Trig . , cos ẞ cos ( — I ) - cos ẞ sin ( 11 — ↓ 1 ) sin B ...

... cone , it will be found that Props . 2 . and 7. apply equally to the oblique cylin- der and oblique cone , to which the de- monstrations may be without difficulty adapted , and hence it may be demon- strated , almost in the words of ...

... power of sin A is written sin 2A , the cube or third power sin 3 , & c . ( 108 ) From the preceding definitions it appears that the sine and cosine of any arc can never exceed the radius ; the secant ... secant thereof . But the tangent of ...

... trigonometric func- tions , 26. Angles corresponding to given functions , 27. Relations between the six trigonometric functions , 30 . CHAPTER III . OF RIGHT TRIANGLES ... Fundamental relations , 36 . Examples and Exercises in Expres ...

John HYMERS (Mathematician). TRIGONOMETRY . SECTION I. THEORY OF TRIGONOMETRICAL RATIOS . OBJECT OF TRIGONOMETRY ... Mathematicians have therefore sought to substitute for them numerical calculations , which always attain the required ...

... h ) 2 or x2 + 2xh + h2 and ( x + h ) 3 = x3 + 3x2 h + 3xh2 + h3 and if the Dinomial is admitted , N- -1 2 then ( x + ... expand any function of ( x + Ax ) into such a form that p ( x + △ x ) — px = A △ x + BAx2 + CAx3 & c . , by ...

... trigonometric func- tions , 26. Angles corresponding to given functions , 27. Relations between the six trigonometric functions , 30 . CHAPTER III . OF RIGHT TRIANGLES . Fundamental relations , 36 . PAGE 1 11 36 Examples and Exercises ...

... Functions in Four Quadrants .. 23. Relations between the Functions of the Same Angle 24. Use of the Preceding Formulæ 25. Graphic Method of finding the Functions in Terms of One .. 26. To find the Trigonometric Functions of 45 ° PAGE 23 ...

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... tangents , and secants . The sine of an angle is a right line let fall from that part of the circle which expresses the angle , upon the diameter of the circle ; as DE is the sine of the angle at c . The secant of an angle is a right ...

... basic , simple relations that follow : ( 1 ) sin 30 ° = 2 ( 2 ) tan 45 ° = 1 since from these two relations the ... TRIGONOMETRIC FUNCTIONS 25.

... characteristic is 1 , and the mantissa .113943 . For reasons which will appear hereafter , only the mantissa of the logarithm is given in a table of logarithms of numbers ; the characteristie must be found by aid of the rules of §§ 70 ...

... formula given in page 67 ; but , in such a construction , an error committed in the sine of an inferior arc would , it is plain , entail errors on the sines of all succeeding arcs . Hence the necessity of some check on the computist ...

... power of sin A is written sin 2A , the cube or third power sin 3A , & c . ( 108 ) From the preceding definitions it appears that the sine and cosine of any arc can never exceed the radius ; the secant ... secant thereof . But the tangent of ...

... Relations between the sides and the angles . Methods of solution Isosceles triangles Special methods PAGE 7 7 8 10 12 12 13 14 16 17 17 17 18 19 23 23 CHAP . III . TRIGONOMETRIC FUNCTIONS OF ANY ANGLE . Generation of angles 30 General ...

... 8. The coversed - sine equals the difference between unity and the sine . 15. Let ABC ( Fig . 2 ) be any THE TRIGONOMETRIC FUNCTIONS . 5 CHAPTER II The Trigonometric Functions Properties and Relations of Trigonometric Functions.

Thomas Grainger Hall. 3. Find the area of a parallelogram , two of its sides being 425 and 320 feet , and smaller ... triangle , and the sum of the other two sides ; find the sides and angles . Ex . Let c = 500 ; a + b = 700 . 9. The area of ...

Thomas Grainger HALL. 2. Find the area of a parallelogram , two of its sides being 425 and 320 feet , and smaller ... triangle , and the sum of the other two sides ; find the sides and angles . Ex . Let c = 500 ; a + b = 700 . 8. The area of ...

... ( ac ) = 193 ° 12 ' 32 " -9 or rather , since ( a + c ) should be greater than ( a – c ) , ( a + c ) = 423 ° 23 ' 3 " -3 ( ac ) 193 ° 12 ' 32 " -9 = * Gauss ( Theoria Motus Corp. Cal . Art . 54 ) recommends the use of the positive sign ...